Calculating device



June 2o, 1939.

A. GoLDsTi-:IN 2,163,032

CALCULATING DEVICE Filed Nov. 16, 1936 2 Sheets-Sheet l Fig. 4.

June 20, 1939. A, GOLDSTElN 2,163,032

CALCULATING DEVICE Filed Nov, 16, 1936 2 Sheets-Sheet 2 /lv 25 121@ 60 62 I la7/4 1 6 (L\ J6 5h 56 i ser e (3k b", lo s Q Z22 y q' 'n u) I' 'f Ff va f S f 7 D wf Q 2 un A m t; g 4 5! i 1 o; 5

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Patented June 20, 1939 PATENT' OFFICE CALCULATING DEVICE Alexander Goldstein, Chicago, lll.

Application November 16, 1936, Serial No. 111,023

Claims.

This invention relates to calculatingl devices and, more particularly, to devices for the vlengths of two-sides of a'triangle'of a given angularity when the length oi one of the sides is known. JMoreparticularly, it relates to a device for calculating the lengths of two sides of a right triangle of a given degree of length of the third side is known.

The device of the present invention may be constructed to indicate lengths in any unit of measure. For convenience I have used the foot as a unit of measure and subdivided the same into inches. In the simplest construction the call culating device is constructed to give the lengths of two of the sides of a triangle when the third side is of a length up to one foot. When the length of the given side is greater than one foot,

or greater than the length of the scale on the device, means must be provided for giving a result which is equal to the additive results for each foot of length of the given side, plus that for the number of inches in excess of the whole number of feet of the given side. It is an object of this invention to provide a device by which this cumulative result may be readily obtained. In that form of construction my unit scale is in the form of a circle' subdivided into twelve sub-units representing inches. The arrangement'is such that the scale is in effectan endless scale wherein one complete turn of the scale is equal to one foot,

, and wherein the result obtained from a calculation jof the fraction of the foot of length of the known side is added to the values resulting from any number of turns in a simple manner, without turning the scale the requisite number of times.

An explanation of the 'construction of the .scales of my device will now be given, from which the attainment of the above and further objects of the present invention will be apparent. l

In the drawings:

Figure 1 illustrates a problem inpipe lengths to be solved by the use of my device;

Figure A2 is a plan of one embodiment of my invention utilizing the'rotating scale;

Figure 3 is a sectional view taken along the line 3 3 of Figure 2; i

Figure 4 is a fragmentary-view of my inven-` tion embodied in rule;

Figure 5 shows a modied construction; and Figure 6 illustrates a fragmentary portion of a longitudinally sliding slide still another embodiment of my"i`nverltlon,v which embodiment is particularly applicable where the angle happens to be 45 degrees. 7

Reference may now be had Amore particularly to Figure l. 'In this ligure I have shown a piping layout comprising a pipe P, anf angular pipe littingQ, another pipe R and a second tting S connesting thepipe R with 'a third pipe T, so that calculating acuteness when the 'tionship of the pipes. A right triangle is formed by the construction -lines A and B wherein the 'line A is at right angles to the pipe P and the line B is parallel to the pipe P. The length A is therefore equal to the oiset between the pipes P and T. In a given construction to be laid out, where the length of the offset A is known and the degree of angularity of the elbow Q is known, it is necessary to calculate the length of the pipe R represented by the side C of the triangle. This may be done by resorting to trigonometric tables which, however, is an impractical method of determining the same since the average pipe itter is not familiar withthe use of tables, and the probabilities of error are veryl great. In order to reduce such possibilities of error I have provided a calculating device which is simple in construction and which may be used by one having comparatively little skill, with only a negligible likelihood of error.

One form of my device is illustrated in Figures 2 and 3, to which reference may now be had. The

calculating'device comprises a plate I0 anda disc II, pivotally joined together bya pivot pin IZ- so that the disc II may turn about the plate I0. An endless circular scale I3 is drawn on the plate I Il about the pivot I 2 as a center. This scale is calibrated to represent one unit of length,

for instance a foot, and is subdivided into s ubunits of length, in this insta'ne inches, of which there are twelve. Each inch is further subdivided the trigonometric ,20

into any convenient number of subdivisions, for I instance sixteen, so that the scale I3 will read in terms of inches and sixteenths of an inch. The 'I Azero point is indicated at I4. 'Ihe disc II h'as a -scaley I5 thereon which is also a circular scale about'the pivot I2 as a center. This scale has a zero mark or index at IB, and the circular scale I5 is subdivided into a number of parts. This scale is so calibrated that when the index I6 is. opposite the index Il the markings on the scale I5,bea r a lxed ratio to the markings at the corresponding` points of the scale I3. The scale I5 is constructed for a trianglepf a -given angularity, in this instance for a triangle wherein the angle V is 221/2 degrees, which means that the angle between A and C is 67%/2 degrees. 'I'he secant of 671/2 de'greesis 2.613. YI therefore construct the scale I5 so that the markings thereof are 2.613 times the markings or values't corresponding parts of the scale I3. It is therefore, apparent that 'when the index marks I 4 and I6 are opposite one another the length of the side C of a 671/2 degree triangle, corresponding to any w cating line I9 is pivoted about the pivot I2 to fa-s cilitate reading of the scales 'I3 and I5. By swinging the pointer I8 to a position such that its indicating line I9 is opposite the point on the scale I3' which corresponds to the length A, or offset of the pipe, the indicating line will be opposite that point on the scale I5 which gives the corresponding length of the line C, or length of pipe required.

I have provided an arrangement whereby my calculating device may be used to calculate lengths even if the offset is more than one foot. In order to illustrate such use-consider, by way of illustration, the oiset A as being of a length of one foot plus X inches. well as from other calculations, it may be as; certained that for one foot oiset the length C should be 31.356 inches or, 2 feet and 7.356 inches. This means that the requisite length of pipe should be 2 feet and 7.35 6 inches plus the necessary length of C to take care of the additional X inches'of oset A. At 'the point 7.356 inches on the scale I5 I have located an index line 20 which has a digit 1, and under it a number 2. When the length A of offset is more than one foot and less than 2 feet the disc'l I is rotated un- A, til the index line 20, marked 1, is opposite the index I4 of the scale I3. The pipe tter then moves will give him the requisite length of pipe in feet and inches. It is apparent that what has been done by shifting the disc II until the index I is opposite the index I4 is to add 7.356 inches to the value of the reading that would otherwise be obtained on the scale I5 corresponding to X inches on the scale I3. Since 2 feet are also added to that number of inches it is apparent that the total addition is 31.356 inches, in terms of feet and inches, which is the length of C corresponding to one foot of A.

If the length of offset A is 2 feet plus X inches the operator turns the disc II until an index line V22 on the disc' II is opposite the index I4. The

location of the index line 22 is obtained, in ther construction of the device, in th'e following manner. Twofeetof length of oset A in this construction is equal to' 62.712 inches of length C,

or 5 feet and 2.712 inches. The line 22 is located at the point on the scale I5 which corresponds to 2.712 inches,.and the number 5 below the number 2v indicates that ve feet must be added to the reading on the scale I5. VIt is thus apparent that by using the index 22, which bears the digit 42 thereon, 2.712 inches are added to the reading on the scale I5 when the indicating line I9 is opposite the value X on the scale I3.

I have locatedindices corresponding tothe indices 20 and 22, these index digits being numbered from 1 to 10 corresponding to the number of feet in the offset A, up to 10, and being located at points on the scale I5 which correspond, in

`terms of the scale I5; to the remainderin inches after the maximum -number of full eetis subtracted from 31.356 inches multiplied by the corresponding digit 1 to 10. Under each on'e of these digits 1 Yto 10 is a number, such as the numbers From this chart, as`

2 and 5 of the digit indices I" and 2,`whichindi cate the number of feet to be added to the value of the reading from the'scale I5 when the corresponding digit has been moved opposite the index I4 and a reading is obtained. By way of example, suppose it `is desired to ascertain the length of the pipe C required for an o ilset of 8 feet and 6 inches. The disc II is rotated until the digit 8, indicated at 24, is opposite the index I4. The

. pointer I8 is turned until the hair line I9 is opposite 6 on the scale I3.` The value on the scale I5 opposite the indicating line I9 is then read, and to that value 20 feet is added.

On the disc I5 there is another scale, indicated at 30. This scale gives the lengths B corresponding to dierent lengths Ain the same manner I that the scale I5 gives the lengths C corresponding to the different lengths A. The scale B is constructed in the same manner' as is the scale A except that the constant instead of being the for two feet, 31 for'three'feet, etc., each one of these indices bearing the numbers 1, 2, 3, etc., indicating the corresponding number of feet in the oiset A for which that index is to be used, and havinga number below the-indicating number,namely the numbers 2, 4, 7, etc., indicating the number of feet to be added to the value of the reading on the scale 3Ilwhen that'corresponding digit index is to be used. The digit index I is located at the point 4.97 inches on the scale 3l),4

which value, 4.97, lis arrived at in the following manner. One foot of-oset A, or 12 inches on the scale I3, is equal to28.97 inches on the scale 30, which is 2 feet and 4.97 inches. I therefore add Y2 feet to the reading to be obtained on the scale 30 and I shift-the index an amount 4.97 inches on the scale 3D when the offset A is more than one foot'and less than 2 feet. Itis thus apparent that the scale 30 is constructed in the s'ame manner as is the scale I5, diierent constants being used.

When reading either the scale I5 or the scale 30 at a time when the digit index on that scale is other than the zero digit index I6, the reading in feet and inches will be correct provided the indicating line I9 on the pointer I8 is not between theindex I6 and the index I4. If the indicating line I9 is between the index I6 and the index I4 then the sum of 31.356 inches must be added to the yreading on the scale I5 in addition to the number of feet indicated below the particular digit index being used. While this addi' tion may readily be made, it is preferable not to require the user of the device to make such addition, but to provide an arrangement so that the-necessity for such addition is obviated and the calculating device gives the added results. To accomplish this I provide an additional set of'digit indices for the scale I5, which set of digit indices correspond respectively to the digit indices I to I0 inclusive on the right hand side of the zero index I6, except that this additional set of digit indices is located` to therleft of the digit index I6. This set of digit indices are also marked I to I0 inclusive. Each one of the digits of this second mentioned digit index is located a distance from the corresponding digit index to the right of the line I6 which is equal to exactly 12 inches measured on the scale I5. Thus the additional digit index I, indicated at 20', .located to the left of the zero index I6 is placed exactly -equal to 1 foot 11 inches.

12 inches from the other digit index I, indicated at 20. This 12 inches is not 12 inches of linear length but 12 inches by the scale I5. Each one of the other vdigit indices to the left of the zero digit index is likewise located 12 inches to the left of the corresponding digit index on the right hand side of the zero index, said 12 inches being measured in accordance with the 'inch scale I5. Each one of the digit indices tothe left oi the zero index has a number -thereunder which is one higher than the number under the corresponding digit index to the right of thevzero index, and indicates the number of feet vt'o be added to the inch reading of the scale I5 when that digit index is used. The scale 30 is likewise provided with a series oi additional digit indices to the left of the zero index, located in the same manner as are-the left hand digit indices of the scale I5, except that the 12 inch unit measure is 12 inches by the scale 30, rather than by the scale I5.

Assume that it is desired to determine the length of pipe C which corresponds to an offset A The disc II is rotated until the digit index' 20 is opposite the digit index I4, and the hair line I8 is brought opposite the 11 inch mark on the scale I3. At this time it is noted that the answer on the scale I5 lies between the zero index. I6 and the zero index I4.

This means that the index 2B cannot be used. Instead the corresponding numbered index 20', which is also numbered I, is to be used. The disc II isv therefore rotated until the indexV 2U' comes under the index I4. The operator then reads the inches on the scale I5 opposite the hair line I9, andI adds 3'feet thereto, which gives him the requisite length of pipe C.

The disc II has been constructed for a piping layout wherein the angle V is 22g/2 degrees. For a dilerent angular construction a different disc must be used in connection with the plate I0. Such diierent disc is laid out in the same manner as is the disc II except-that for its scale I5 the constant used is the consecant of the particu lar angle V and for the scale 30 the constant used is the cotangent of that angle. In ordinary pipe work the number of dilerent angles encountered is quite few. Therefore, by providing a half a dozen or so different discs II in connection with the single plate I all probable arrangements to be encountered can be taken care of.

The disc I I and the plate I0 are held together by a knurled nut on the pivot I2, which may be removed in order to change discs II.

While it is desirable that the digit indices, such as the digit index 20, be located on the scale I this is not indispensible. For instance, when the digit index 20 is moved to a position opposite the index I4 on the scale I3, the zero indexI I5 is opposite the point 9.18 on the' scale I3. It is therefore apparent that the results above described can be. obtained by locating the 'digit index 20 at the point 9.18 on the scale I3 and then instructing the user of the chart to move the disc II until the zero point I6 comes opposite the digit index at that point on the scale I3. Such `an arrangement; however, is' less desirable than the present arrangement because that would preclude using the same plate I0 for different discs I5 corresponding to different angular pipe layouts.

A'ns

. In Figure 4 I have illustrated the principles of the present invention applied to a longitudinally moving slide rule. In this instancethe scales 40 and 4I correspond `to thefscale I3, whereas4 the -previously occupied by the scale 30.

scales 42 and 43 correspond to the scales II and 30, respectively, and are laid out in exactly the same manner. The usual hair line indicating type of sliding carriage is provided with the' slide rule. In this slide rule the slidable member 44 correspondsto the disc II and may be replaced by another member 44 calibrated for a diiIerent particular angle for the triangle A-B-C. In this case thescales 42 and 43 'are provided with a plurality of digit indices corresponding to the respective digit indices on ,similarly located.

In Figure 5 I have shown a modified construction wherein the necessity for the digit indices to the left of the index I6 is dispensed with. This result is obtained by making the scale 50, which corresponds to the scale I3, of a length of two feet, instead of one foot.\length. The scales 5I and 52 are, therefore, also of a length twice that oi the corresponding scales I5 and 30 of Figure 2. In other respects this device is exactly the .same as that of Figure 2, and is used-in the same manner.

In Figure 6 I have shown still another construction, which is particularly applicable where the angle of the oii'set is exactly 45 degrees, which means that the length B is equal to the oiset A, and no B scale need be provided, hence a scale corresponding to the scale 30 of Figure 2 is. omitted. When this is the case I can avoid the need of `the second group of digit indices "which are located to the left of the index I6 in Figure 2, by continuing the scale 60, which corresponds to the scale I5, from the I6 index line around a complete circle and then continuing the same below the line 6I, which is the lspace 'I'hus if the answer is to be read on the scale 60 at a point betweenthe digit index' I6 and the zero point I4, then the operator reads the portion of the scale below the line 6I- rather than the portion of the scale above that line.

While I have chosen to illustrate my present invention in connection with an embodimenty wherein the unit of length is taken as a foot Y and the sub-units thereof are taken as twelfths of a foot, it is to be understood that this is merely illustrative of the principles of the invention, as

any other units or sub-units. may be used.

In compliance with the requirements of the patent statutes I have here shown and described 'a few preferred embodiments oi my invention. It is, however, to be understood that the invention is not limited tothe precise'constructions here shown, the same being merely illustrativeof the principles of the invention. What I consider new anddesire to secure by Letters Patent is:

1. A device for determining the length of aside of a right angle triangle of a given angularity When the length of another side is known, said device comprising two relatively movable slide members having adjacent relatively movable scales the rst of which is calibrated into subunits of at least one complete unit of measure and the second ofwhich is calibrated as a constant multiple of said first scale, the constant being the ratio of the lengths of the two sides of a right angle triangle of the angularity for which the device is constructed, whereby when the vzero index marks'of the two-scales arev opposite one another the adjacent values on the two scales indicate corresponding lengths of two sides of said triangle up to a unit of length of one of said sides, one of said scales having a series of other index marks thereon constituting digits, each digit index being spaced from the zero point on the scaleby a distance which is equal in length, in sub-units of the second scale, to the remainder after the largest possible numberof whole units has been subtracted from the product of the digit and the constant multiplied by the number .of sub-units per unit, said maximum number of whole units being indicated adjacent each' digit index.

2. A device for determining the length of a I side of a right anglev triangle of a given angularity when the length of another side is known, said device comprising two relatively movable slide members having adjacent relatively movable scales the rst of which is calibrated into sub-units of at least one complete unit of measure and the second of which is calibrated as a constant multiple of said first scale, the constant being the'ratio ofi-the lengths of the two sides of a right angle triangle of the angularity for which the device is constructed, whereby when the zero index marks of the two scales are opposite one another the adjacent values on the two scales indicate corresponding lengths of twosides of said right angle triangle up toa unit of length of one of said sides, one of said scales having a series of other index marks thereon constituting digits, each digit index being spaced from' the zero point on the scale of a distance which is equal Iin length, vin sub-units of the'second scale, to the remainder after the largest possible number of wholev units has been subtracted from the product of the digit and the constant multiplied byl the number of sub-units per unit, said maximum number of Whole units being indicated adjacent each digit index, a third scale on the member which has the second scale, said third scale being also adjacent said first scale but calibrated as a different constant multiple of 4the iirst scale, said different constant being the ratio of the length of the third side of the triangle to that of the known side, a second series of digit indices for said third scale, and means for indicating points on either of the two last mentioned scales corresponding to a desired point on the rst scale.

3. A device for determining the length of a side Aof a right angle triangle of a given angularity when the length of anotherside is known, said device comprising two superimposed relatively rotatable members, one of said members having a circular scaledivided into sub-units of measure, the second memberhaving a circular scale oppositev said rst scale and calibrated as a constant multiple of said first scale, the constant being the ratio of the llengths of the two sides of ,a right angle triangle of the angularity for which the device is constructed, whereby whenthe zero'points of the two scales are opposite one another the adjacent values of the two scales indicate correspending' lengths of two sides of said right angle triangle up to a unit length of one of the sides,

one of said members having a series of other in-` dex marks thereon constituting digits, each digit Aindex being spaced from the zero point on the device comprising two adjacent relatively movable members, one lof said members having a scale divided into sub-units of measure, the other member having a scale opposite said first scale and calibrated as a constant multiple of said rst scale, the constant being the ratio of the lengths of the two sides of a right angle triangle of the angularity for whichl the device is constructed, whereby when the zero points of the .two scales are opposite one another the adjacent values of the two scales indicate corresponding lengths of two sides of said right angle triangle up toa unit length of one of the sides, said second member having a series `of other index marks thereon bearing digits, each digit index being located at the point on the scale of the second member Awhich indicates the remainder in sub-units after the maximum number of whole units has been subtracted from the product of the digit and the constant multiplied by the sub-units per unit, said maximum numberof whole units being indicated adjacent each digit index.

5. A device for determining the length of a side of a right angle triangle of a given angularity when the length of another side is known, saiddevice comprising two adjacent relatively movable members, one of .said members having a scale divided into sub-units of measure, the second member having a scale opposite said rst scale and calibrated as a constant multiple of said first scale, the constant being the ratio of the lengths of the two sides of a right angle triangle 'of the angularity for which the device is constructed, whereby -when the zero points of the two scales are opposite one another the adjacent values of the two scales indicate corresponding lengths of two sides of said right angle triangle up to a unit length of one of the sides, said second member having a series of other index marks thereon, bearing digits, each digit index being located at the point on the scale of the second member which indicates the remainder in subunits after the maximum number of whole units has been subtracted from the product of the digit and the constant multiplied by the sub-units per unit, said maximum number of whole units being indicated adjacent each digit index, said second member having another scale thereon constructed in the same manner as is the rst scale thereon but a different constant multiple of the first scale, which second constant is the ratio of the length of the third side to that of the known side of the triangle for which the'device is 'constructed. ALEXANDER GOLDSTEIN. 

